Level lowering for half-integral weight modular forms
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- by Jim Brown and Yingkun Li PDF
- Proc. Amer. Math. Soc. 138 (2010), 1171-1173 Request permission
Abstract:
In this paper we provide a level lowering result for half-integral weight modular forms. The main ingredients are the Shimura map from half-integral weight modular forms to integral weight modular forms along with a level lowering result for integral weight modular forms due to Ribet. It is necessary to keep track of the parity of the weight as well as the character involved so that one can apply the Shintani lift to go back to a half-integral weight modular form and establish the result.References
- M. Manickam and B. Ramakrishnan, On Shimura, Shintani and Eichler-Zagier correspondences, Trans. Amer. Math. Soc. 352 (2000), no.Β 6, 2601β2617. MR 1637086, DOI 10.1090/S0002-9947-00-02423-5
- Kenneth A. Ribet, Report on mod $l$ representations of $\textrm {Gal}(\overline \textbf {Q}/\textbf {Q})$, Motives (Seattle, WA, 1991) Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp.Β 639β676. MR 1265566, DOI 10.1090/s0273-0979-1994-00465-3
- Goro Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440β481. MR 332663, DOI 10.2307/1970831
Additional Information
- Jim Brown
- Affiliation: Department of Mathematical Sciences, Clemson University, Clemson, South Caro- lina 29634
- Email: jimlb@clemson.edu
- Yingkun Li
- Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
- Address at time of publication: Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, California 90095-1555
- Email: yingkun@caltech.edu, yingkun@math.ucla.edu
- Received by editor(s): January 14, 2009
- Published electronically: December 9, 2009
- Additional Notes: The authors would like to thank the referee for suggestions on how to strengthen and streamline the original arguments.
The second author was supported by a Summer Undergraduate Research Fellowship at California Institute of Technology and the John and Maria Laffin Trust. - Communicated by: Wen-Ching Winnie Li
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1171-1173
- MSC (2010): Primary 11F37, 11F80
- DOI: https://doi.org/10.1090/S0002-9939-09-10242-3
- MathSciNet review: 2578511